From the recent experimentally observed conduction band offset and previously reported band gaps, one may deduce that the valence band offset between rutile SnO₂ and TiO₂ is around 1 eV, with TiO₂ having a higher valence band maximum. This implication sharply contradicts the fact that the two compounds have the same rutile structure and the Γ₃⁺ VBM state is mostly an oxygen p state with a small amount of cation d character, thus one would expect that SnO₂ and TiO₂ should have small valence band offset. If the valence band offset between SnO₂ and TiO₂ is indeed small, one may question the correctness of the previously reported band gaps of SnO₂ and TiO₂. In this paper, using first-principles calculations with different levels of computational methods and functionals within the density functional theory, we reinvestigate the long-standing band gap problem for SnO₂. Our analysis suggests that the fundamental band gap of SnO₂ should be similar to that of TiO₂, i.e., around 3.0 eV. This value is significantly smaller than the previously reported value of about 3.6 eV, which can be attributed as the optical band gap of this material. Similar to what has been found in In₂O₃, the discrepancy between the fundamental and optical gaps of SnO₂ can be ascribed to the inversion symmetry of its crystal structure and the resultant dipole-forbidden transitions between its band edges. Our results are consistent with most of the optical and electrical measurements of the band gaps and band offset between SnO₂ and TiO₂, thus provide new understanding of the band structure and optical properties of SnO₂. Experimental tests of our predictions are called for.